The present invention relates to filtering seismic data, in particular by kriging analysis.
Kriging analysis enables a random function to be resolved from its covariance function.
In particular, it is conventionally used in geostatistics for filtering seismic data, particularly but in non-limiting manner, for characterizing reservoirs.
Kriging analysis relies in particular on the assumption that a phenomenon measured locally by means of optionally-regular sampling can be analyzed as a linear sum of a plurality of independent phenomena, the variogram of the overall phenomenon corresponding to the linear sum of the variograms of each of the independent phenomena making it up.
Conventionally, the variogram corresponding to the measured experimental data is resolved as sum of modeled variograms, and from the experimental data and the models selected for the individual variograms used to resolve the data, there are deduced the individual functions that make up the random function corresponding to the overall phenomenon.
It is thus possible to extract from a seismic data map of the type shown in FIG. 1 (e.g. raw experimental data) firstly the white noise that is present in the data (FIG. 2a), secondly noise corresponding to linear lines (FIG. 2b), and finally filtered data cleared of both of these kinds of noise (FIG. 2c).
The kriging calculations for determining the values of the individual functions into which an overall random function is resolved are themselves conventionally known to the person skilled in the art.
In this respect, reference can be made, for example, to articles and publications mentioned in the bibliography given at the end of the present description.
Very generally, the value of an individual function involved in making up the overall random function is determined as being a linear combination of experimental values for points in an immediate neighborhood of the point under consideration, these experimental values being given weighting coefficients.
In other words, if it is considered that a function Z(x) is made up as the sum of individual functions Yu(x), this can be written:
      Z    ⁡          (      x      )        =            ∑              u        =        1            U        ⁢                  Y        u            ⁡              (        x        )            and the component Yu(x) is estimated by:
            Y              u        *              ⁡          (      x      )        =            ∑              α        =        1            N        ⁢                  λ        u        α            ⁢              Z        α            where α is a dummy index designating the points under consideration around the point x for which it is desired to determine the estimated value Yu*(x), Zx being the value at the point x, N being the number of such points.
It can be shown that the weighting coefficients λα satisfy the equation:
            (                                                  C              11                                            …                                              C                              1                ⁢                N                                                                          ⋮                                                                                          ⋮                                                              C              N1                                            …                                              C              NN                                          )        ⁢          (                                                  λ              u              1                                                            ⋮                                                              λ              u              N                                          )        =      (                                        C            01            u                                                ⋮                                                  C                          0              ⁢              N                        u                                )  where the index 0 designates the point for which an estimate is to be determined, the values C01u to C0Nu being the covariance values calculated from the model u corresponding to the component Yu (values of the covariance function for the distances between each data point and the point to be estimated), the values Cij being covariance values calculated as a function of the selected model for the variogram of the function to be estimated (values of the covariance function for the distances between the data points).
These weighting coefficients λux are thus determined merely by inverting the covariance matrices.